Q. The area (in square unit) of the region bounded by the curves $2x = y^{2} - 1\ and\ x = 0$ is
A) $\frac{1}{3}\ sq\ unit$
B) $\frac{2}{3}\ sq\ unit$
C) $1\ sq\ unit$
D) 2 sq units
Explanation
(b)
Given curve can be rewritten as
$y^{2} = 2\left( x + \frac{1}{2} \right)$
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$\therefore Required\ area = \int_{- 1}^{1}{x\ \ dy}$
$= 2\int_{0}^{1}{\frac{y^{2} - 1}{2}dy}$
$= \left| \left\lbrack \frac{y^{3}}{3} - y \right\rbrack_{0}^{1} \right|$
$= \frac{2}{3}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.